Controlling a plant invader by targeted disruption of its life cycle

Authors

  • Joseph T. Dauer,

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      Correspondence author: Department of Plant Biology, Michigan State University, Plant Biology Laboratories, 612 Wilson Road Room 166, East Lansing, MI 48824, USA. E-mail: jdauer@msu.edu
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  • Peter B. McEvoy,

    1. Department of Botany and Plant Pathology, Oregon State University, 2082 Cordley Hall, Corvallis, OR 97331 2902, USA
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  • John Van Sickle

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    • Department of Fisheries and Wildlife, Oregon State University, Corvallis, OR 97333, USA.


Correspondence author: Department of Plant Biology, Michigan State University, Plant Biology Laboratories, 612 Wilson Road Room 166, East Lansing, MI 48824, USA. E-mail: jdauer@msu.edu

Summary

1. Pest management strategies should be informed by research on a broad suite of biotic and abiotic interactions. We used a life table response experiment (LTRE) to assess the reliability of ragwort Jacobaea vulgaris management recommendations based on interactions of (i) time of disturbance to initiate experimental units, (ii) herbivory from two biological control organisms, the cinnabar moth Tyria jacobaeae and ragwort flea beetle Longitarsus jacobaeae and (iii) interspecific competition by perennial grasses.

2. Our LTRE combines a factorial experiment with a linear, deterministic matrix model for ragwort populations representing transitions among three stages: 1st year juveniles, ≥2nd year juveniles and adults. Elasticity analysis identified potentially vulnerable ragwort transitions, and a contributions analysis confirmed which treatments influenced these transitions. Ultimate treatment effects were quantified as the reduction in population growth rates and time to local extinction.

3. Elasticity analyses found the ragwort’s biennial pathway, juvenile to adult transition and fertility transition were most influential and most amenable to manipulation across all community configurations. The flea beetle and perennial grass competition had negative effects on survival and fertility, whereas the cinnabar moth only reduced fertility and induced the perennial pathway.

4. All combinations of insects or increased plant competition reduced the growth rate of ragwort. Full interspecific competition and the flea beetle resulted in a significantly greater and faster decline in the ragwort populations than the cinnabar moth. Moreover, this pattern was consistent between two times of initial disturbance.

5.Synthesis and applications. Maximizing plant competition provides the fastest way to control ragwort. If this option is unavailable, for example, grazed or disturbed land, the ragwort flea beetle provides excellent management to lower ragwort densities without the potential nontarget effects of the cinnabar moth. Factorial experiments and matrix models help to evaluate interacting factors that influence invasive species’ vulnerabilities, inform how to intervene in a weed life cycle to reduce weed abundance and confirm recommendations that are robust to community variation.

Introduction

The causes, consequences and cures of biological invasions have received attention from ecologists for decades (Elton 1958; Williamson 1996; Shigesada & Kawasaki 1997; Myers & Bazely 2003; Davis 2009). Biological invasions are likely to be the result of many factors – including attributes of the invading organism, the recipient environment, and society – but ecologists do not yet fully understand the interaction of these factors. As biological control organisms become an increasingly important factor, a major challenge is to weigh the importance of biological control organisms relative to other options for invasion management (Paynter & Flanagan 2004).

Successful biological control of weeds results from inhibition of weed outbreaks by insect herbivory and plant competition outweighing their activation by local disturbance and colonization from a seed source, also known as the activation–inhibition hypothesis (McEvoy et al. 1993). In this study, we explore the ecological and demographic mechanisms underpinning successful biological control of Jacobaea vulgaris L. (formerly known as Senecio jacobaea L., Asteraceae) in the Western USA. Following successful biological control, weed populations are at such low levels that the role of herbivores and competitors may not be obvious (Harper 1977). The forces maintaining weed populations at low levels cannot be detected by passive observation alone; a population needs to be perturbed to reveal the forces that maintain it. Perturbations in this study were selected to mimic the range of community configurations where J. vulgaris (hereafter ragwort) might thrive or be forced to local extinction. There was a single, high intensity disturbance (tilling) to set the stage for colonization of ragwort seedlings from the seed bank (McEvoy & Rudd 1993; McEvoy et al. 1993). Plant competition was subsequently removed, reduced or left unaltered, and herbivory levels were defined by the presence/absence of the two most prevalent biological control organisms for ragwort.

Populations unrestrained by competitors or natural enemies should grow quickly, and adding competitors and insect herbivores should slow ragwort’s population growth rate. Ragwort ranges from a biennial to short-lived perennial, and we hypothesize that competitors and natural enemies that specifically influence biennial life cycle transitions will have the greatest impacts on ragwort growth rate for a population invading new territory (Davis et al. 2006). We first confirm these vulnerabilities, then explore to what extent competitors and natural enemies affect these vulnerabilities before finally quantifying the effects on population growth rate and extinction.

Population matrix models translate individual effects to population level dynamics where matrix elements represent life cycle transitions among life stages. Such models have been used as an explanation and guide for conservation biology (Mills, Doak & Wisdom 1999) and invasive species management, including biological control. In a recent review by Crone et al. (2011), 13 of the 158 management-focused studies explored species interactions with matrix models, but none explored biological control and interspecific plant competition simultaneously. After parameterization of a matrix model, perturbation analyses can be used to identify individual stages and transitions that could be manipulated to reduce population growth and spatial spread of nonindigenous plants and animals (Byers et al. 2002; Miller & Tenhumberg 2010).

A life table response experiment (LTRE) combines a factorial experiment and a matrix model to test how single or multiple factors affect ragwort population dynamics. The aim of this study is to (i) improve the application of ecology to invasive weed control and (ii) prioritize management scenarios for a pasture weed. Recommendations will be based on analysis of causes (interacting factors that can be used to target ragwort vulnerabilities) and effects (short-term extinction and long-term population growth rates). Researchers often present pest population growth rates for their treatments and then explore explanations for treatment effects (Buckley et al. 2005; Jongejans et al. 2008). Our approach reverses this order by identifying vulnerable life cycle transitions of pests to prioritize management prior to testing which treatments influence those vulnerable transitions, and which are successful in reducing weed abundance. We highlight an experimental and analytical approach that can be generalized to prioritize management options for invasive species influenced by many interacting factors.

Materials and methods

Study System

The biological details of the study system are reviewed elsewhere (McEvoy et al. 1993) and only summarized here. Ragwort is a biennial or short-lived perennial herb introduced into the Pacific Northwest of the United States from Europe. For the past five decades, ragwort has been regarded as a noxious weed in rangelands and natural areas throughout the west coast of North America from British Columbia to northern California. Management options include chemical treatment, pasture management to increase competition and insect herbivores released for biological control (Wardle 1987; Bain 1991; Leiss 2011). Three insects were established for ragwort control (Pemberton & Turner 1990; McEvoy, Cox & Coombs 1991): Tyria jacobaeae (L.) (Lepidoptera: Arctiidae) (cinnabar moth), Botanophila seneciella (Meade) (Diptera: Anthomyiidae) (ragwort seed-head fly, formerly Hylemia seneciella) and Longitarsus jacobaeae (Waterhouse) (Coleoptera: Chrysomelidae) (ragwort flea beetle). We concentrate on the two most successful control organisms: the cinnabar moth and ragwort flea beetle. Larvae of the cinnabar moth are leaf and flower feeders. Adults of the flea beetle are pit feeders, rasping holes in leaves of mainly juvenile plants, while larvae develop by feeding on leaves, petioles, stems and roots. The plant community in our study was typical of coastal pastures and grasslands in the Pacific Northwest, supporting a dense cover dominated by introduced and widely established perennial grasses Holcus lanatus L., Dactylis glomerata L., Anthoxanthum odoratum L. and Schedonorus phoenix (Scop.) Holub (=Festuca arundinacea Schreb).

Factorial Experiment

The factorial experiment consisted of two disturbance times (Autumn 1986 and Spring 1987) × 3 levels of plant competition (background vegetation Unaltered, Clipped or Removed) × 2 levels of cinnabar moth herbivory (plants Exposed or Protected using exclusion cages) × 2 levels of ragwort flea beetle herbivory (plants Exposed or Protected using exclusion cages) × 4 blocks = 96 experimental units (McEvoy et al. 1993; McEvoy & Coombs 1999). Disturbance of 0·5 × 0·5 m plots was achieved by tilling the soil to ‘reset’ the vegetation succession and initiate experimental units of autumn-emerging and spring-emerging ragwort plants from the pool of seed buried in soil. Individual ragwort plants were mapped as they emerged and followed in a longitudinal census for 4 years from 1986 to 1990. Over 97% of the 4208 plants emerged within 3 months of the initial disturbance time, and the ultimate fate was known for 99% of emerged seedlings. Plants were protected from herbivores by cages that could be opened or closed to prevent access by the cinnabar moth (active in summer) or ragwort flea beetle (active autumn through spring). Herbivore-exclusion cages allowed seed dispersal within experimental plots, but prevented seed dispersal among experimental plots, thereby preserving the independence of experimental units assumed in statistical analyses. To manipulate plant competition, background vegetation was either left unaltered, clipped using grass shears to maintain a height of 5 cm or removed by hand pulling. Clipping was used to simulate grazing by ungulate herbivores. The response to experimental manipulations was measured as demographic rates (raw data) of emergence, growth, development, survivorship, reproduction and recruitment. There were no consistent differences in population matrices between experimental units started in Autumn 1986 and Spring 1987; we report results separately to recognize effects of initial conditions on specific interacting factors.

Development, Analysis and Interpretation of the Matrix Model

The primary purpose of our mathematical model was to describe the dynamics of our experimental ragwort populations. The full life cycle graph for ragwort depicts four stage classes and nine annual transitions among stage classes (Fig. 1). There are four classes of ragwort individuals: dormant seed (D), first-year juveniles (J1), second-year or older juveniles (J2), and adults (A). Life cycle transitions are represented using discrete rather than continuous classification of individuals. All individuals in the initial cohort of J1 were recruited from individuals in stage D. We created two juvenile classes J1 and J2 after finding they had different probabilities of development and survival (i.e. the joint probability S1*S2*S3 associated with the perennial pathway differs from the probability S4 associated with the biennial pathway).

Figure 1.

 Ragwort life cycle. Life cycle graph showing four stages and nine transitions in ragwort’s life cycle. The four stages are D dormant seed, J1 1st year juveniles, J2 juveniles ≥2 year old and A adults. The biennial pathway is composed of two transitions F and S4; the perennial pathway is composed of three transitions S1, S2 and S3; iteroparity is symbolized by S5; and the dormancy pathway is composed of three transitions D6, D7 and D8. Populations in our experiment started with a pulse of recruitment from stage D, with no recruitment from this source thereafter. The iteroparity pathway (S5) was not expressed in our experimental populations.

The D stage is excluded from the model for this environment, assuming a pulse of recruitment from the long-lived seed bank occurs in year 1 but not thereafter. The experiment was implemented in a field with no flowering plants, but with a large buried seed pool as a legacy of the historical abundance of ragwort. Experimental units were established from the seed bank (seeds that were >1 year old) and not the seed rain (seeds that were 1 year old). Conversely, subsequent recruitment was from seed rain but not seed bank. Recurrent disturbance is required to move seeds from the seed bank to the surface where they may germinate, and its absence effectively uncoupled the seed bank from the actively growing plant population (McEvoy & Rudd 1993). The fertility transition (F) is a compound parameter in our model, including probability of flowering, pollination, seed production, germination, seedling emergence and survival to the J1 stage. A linear, deterministic matrix (A) was parameterized for each experimental unit using the raw data and represented the stages and transition among stages (aij) shown in the life cycle graph.

image(eqn 1)

The stage-structured matrix projects how the number of individuals in each stage (nt = [J1, J2, A]) will change from 1 year t to the next + 1 : n+ 1 = A*nt (Caswell 2001). Projection matrices were estimated for each of the 96 experimental units (see Appendix S1, Supporting Information). Individuals at each stage from four replicate units were pooled following the convention of Brault & Caswell (1993), and the projection matrices for each treatment were estimated. Each experimental unit was treated as a replicate of an independent population because experimental units contained sufficient ragwort densities to estimate parameters, and experimental units were isolated from each other by herbivore-exclusion cages.

Prospective analyses of projection matrices (A) estimate demographic parameters (growth rate, extinction times, sensitivities, elasticities) that determine a population’s dynamics (Caswell 2001). The asymptotic growth rate in the population is represented by the dominant eigenvalue (λ) of A, and populations increase exponentially (λ < 1), remain steady (λ = 1) or decrease exponentially (λ < 1), with time.

Sensitivity and elasticity can be used to determine the effects of small perturbations to each transition rate in A on population growth rates λ. Sensitivity (sij) is the change in λ owing to a small change in matrix element aij:

image(eqn 2)

Elasticity (eij) is the proportional change in λ owing to a small proportional change in matrix element aij (Caswell 2001):

image(eqn 3)

The elasticities of a projection matrix sum to one across all transitions in the matrix.

We assumed that the goal of biological control is to eliminate plants from an area of management, for example, pasture or agronomic field. For this goal, we apply the term local extinction, and we use projected time to local extinction as a measure of the speed of control (McEvoy & Coombs 1999). Time of local extinction was defined operationally as the time step in which all stages had less than one above-ground individual (McEvoy & Coombs 1999). Population change was projected for populations that were declining (λ < 1), but had not yet reached local extinction at the completion of our experiment, initializing population density using the number of individuals in the J1 stage in 1987 and setting abundances for other stages to 0.

Retrospective analyses are complementary to prospective analyses (Caswell 2001) and give the contribution of change in life cycle transitions to observed differences in λ between a control and the treatment. High sensitivity implies a potential for a transition to influence λ, whether it actually does so depends additionally on the realized effect of the treatment on the transition (eqn 4). A transition may make a larger contribution to changes in λ because of either large treatment effect, high sensitivity or both. The contribution can be decomposed into the difference of matrix elements (aij) and the sensitivity of the projection matrix midway between the treatment (k) and control (c):

image(eqn 4)

The magnitude of a single matrix element contribution depends on the observed difference of the treatment transition rate inline image relative to the population mean or experimental baseline inline image (Levin et al. 1996; Munzbergova 2007). The experimental control is the baseline growth rate from which to evaluate how transitions were affected by a treatment. The neither-herbivore treatment was set as the baseline to compare herbivore treatments and the removed-plant-competition treatment as the baseline to compare competition treatments.

We used data resampling (bootstrapping) to estimate means and 95% confidence intervals for growth rates, extinction times, sensitivities, elasticities and life-cycle-transition-rate contributions (Manly 1991). Individuals within a plot were randomly sampled from the raw data, with replacement, pooled as done previously, and transition rates estimated to give a bootstrap projection matrix Abs. Demographic parameters were estimated from Abs, and the process was repeated 2000 times. The arithmetic mean and confidence intervals were estimated using the percentile method and not bias-corrected because the mean and median were approximately equal (Efron & Tibshirani 1993). For the life-cycle-transition-rate contribution analysis, raw data from the treatment (k) and control (c) were resampled, pooled within treatment and control, and then converted into matrices inline image, inline image. Using eqn 4, the bootstrapped contributions were estimated and repeated 2000 times. Nonoverlapping confidence intervals were used as a criterion of significance to test interaction effects of interspecific plant competition and herbivory. This procedure should be regarded as exploratory rather than confirmatory, as the degrees of freedom were insufficient to test all possible interaction terms using permutation tests (Manly 1991). Demographic parameters and simulations were estimated using R computer software with code written specifically for this research and utilizing the popbio library (R Development Core Team 2011).

Results

Potential Causes of Ragwort Decline

Elasticity and sensitivity highlight the potential importance of transition rates in long-term population dynamics (Fig. 2, Appendix S2, Supporting Information). Unaltered competition was so overpowering at this site that the life cycle could not be completed and elasticity could not be estimated for 36 of 96 (37%) experimental units, with 32 experimental units experiencing Unaltered background vegetation and four experimental units experiencing Clipped background vegetation (Fig. 2). When background vegetation was Removed or Clipped, the relative importance of transitions varied by herbivore species. Elasticities associated with the biennial pathway (S4 and F) were greater than those associated with the perennial pathway (S1, S2, and S3) in 13 of 15 treatment combinations. The major exception was the Moth treatment where two of four treatment combinations with the Moth had greater elasticity in the perennial transitions. In the Removed, Neither treatment, the highest elasticities were associated with S4 and F. Overall, S4 and F were potentially the most influential transitions, that is, their manipulation could result in the greatest effect on population growth.

Figure 2.

 Life cycle elasticity. The bootstrapped elasticity (95% confidence intervals) of stage transitions (S4, F, S1, S2 and S3; Fig. 1) for (a) Autumn and (b) Spring disturbance. Bars represent percentage of the total elasticity associated with each transition. The dashed lines represent the mean sum (confidence intervals not shown) of elasticities for the biennial pathway (S4 and F, grey bars) and perennial pathway (S1, S2, and S3, white bars), and show the potential importance of each pathway to changes in population growth rates.

Realized Causes of Ragwort Decline

While sensitivity and elasticity can assess which transitions could potentially cause a change in plant growth, a contributions analysis quantifies which transitions actually had the greatest effect on the observed growth rates. A few treatments contributed positively to changes in λ, but the magnitudes of positive contributions were small relative to the magnitudes of negative contributions, dominated by the F and S4 contributions (Fig. 3). Surprisingly, perennial transitions could potentially influence ragwort populations exposed to the cinnabar moth, judging by elasticity (Fig. 2), but did not actually do so because perennial plants were uncommon in this study (Fig. 3). The observed growth rate differences in the Moth treatments were due almost exclusively to decreases in fertility that is expected because the cinnabar moth effectively inhibits seed set, while the S4 contribution was minimal because the caterpillars of the cinnabar moth have little effect on rosettes. On the other hand, the flea beetle is a foliar feeder as adult and a root feeder as larva, and reductions in the S4 and F transitions made equal contributions to decline in growth rate in three of the four plant competition levels (Fig. 3) as predicted by the elasticity analysis (Fig. 2).

Figure 3.

 Herbivory contributions. The bootstrapped contributions (95% confidence intervals) of stage transitions to change in growth rate relative to neither-herbivore treatment for (a) Autumn and (b) Spring initial disturbance. Biennial transitions (grey bars, S4 and F) always made a greater contribution than the perennial transitions (white bars, S1, S2 and S3).

Analysis of contributions in the both-herbivore treatment could determine whether the cinnabar moth or beetle was having a greater impact on reducing growth rate by reducing the biennial transitions identified for this treatment (Fig. 2). In three of four both-herbivore treatments, herbivory acting on F and S4 collectively had the greatest contribution to decline in λ (Fig. 3). This suggests that the two herbivore species are better for controlling ragwort than either one acting alone, and they may be regarded as complementary rather than antagonistic.

A similar contributions analysis was used to examine which matrix elements impacted the growth rate differences between Removed background vegetation and the Clipped vegetation but not the Unaltered vegetation, where growth rates of zero prevented analysis. Perennial transitions had minor impacts on the difference in growth rate, but biennial transitions were very important (Fig. 4), as predicted by their elasticities (Fig. 2). Competition severely reduced the S4 transition, preventing many juveniles from maturing into adults. Plots disturbed in the autumn allowed ragwort to get a head start on growth, and those surviving competition benefited by increasing their fertility especially when herbivores were absent or just the cinnabar moth was present. Spring disturbance had the opposite effect, and reduction in F had an equal or greater impact to S4 inhibition on growth rates.

Figure 4.

 Competition contributions. The bootstrapped contributions (95% confidence intervals) of stage transitions in clipped background vegetation to change in growth rate relative to removed-competition treatment for Autumn and Spring initial disturbance. Biennial transitions (grey bars, S4 and F) always made a greater contribution than the perennial transitions (white bars, S1, S2 and S3).

Impacts of Interspecific Competition and Herbivory

Elasticity analysis informs researchers of the possible ecological mechanisms operating in this complex system, but managers of ragwort are primarily interested in which single or multiple treatment factors will have the greatest impact on reducing ragwort population density. Ragwort populations had λ ≥ 1 in six treatments where competition and natural enemies were reduced or absent (Fig. 5). Population growth rates were significantly affected by the independent and interacting effects of time of initial disturbance and the levels of background vegetation and insect herbivory (Fig. 5). There were no consistent differences overall between populations started in autumn and those started 6 months later in the spring; matched by treatments, λ in Autumn < Spring (four cases), Autumn = Spring (seven cases) and Autumn < Spring (one case).

Figure 5.

 Population growth rate (λ). The bootstrapped proportional change (95% confidence interval) in population size per year for (a) Autumn and (b) Spring initial disturbance. λ > 1 signifies exponential increase, λ = 1 indicates no change (stasis) in population size, and λ < 1 indicates exponential decrease.

The other 18 treatment combinations resulted in population growth rates significantly below 1, indicating successful control, by either plant competition, natural enemies or both (Fig. 5). In general, the effects of the herbivores emerge more clearly as plant competition was reduced (moving right to left in Fig. 5), and the effects of competing plant vegetation emerge more clearly as the flea beetle was removed (moving from bottom to top). The growth rates for all ragwort populations converged to zero when the competing vegetation was Unaltered, but less competition (Clipped) resulted in greater λ (Fig. 5). The cinnabar moth and ragwort flea beetle each reduced ragwort population growth, the beetle more so than the cinnabar moth. The cinnabar moth alone yielded inconsistent results with only half the populations having growth rates below one (considering the 95% CI), while the beetle alone consistently reduced ragwort growth rates below 1 (Fig. 5).

Reducing time to local extinction is a desired outcome for biological control in theory and practice. Increased competition (going from top to bottom, Fig. 6) had a strong effect, and unaltered competition resulted in extinct (no more above-ground plants) populations after 2–4 years. Herbivore effects were strong and additive (moving from left to right, Fig. 6). The beetle caused greater population extinction than the cinnabar moth, and the combined effect (Beetle + Moth) was also greater than the Moth alone. Projected population lifetimes correspond well with observed lifetimes (Fig. 6). Lifetimes could be predicted for population with growth rates near 1 but not extinct by the end of the experiment. For example, the Autumn disturbed, Clipped vegetation and Beetle treatment had a mean time to extinction of 4·04 years, and the Spring disturbed, Clipped vegetation and Moth treatment had a mean time of 5·67 years. Populations with growth rates close to 1 (Fig. 5) were projected to survive 40 or more years, assuming static environmental conditions.

Figure 6.

 Time to ragwort extinction. Proportion of simulated populations (open symbols) projected to go extinct within 1–4 years and proportion of total populations (out of four possible) that were observed to go extinct (filled symbols, McEvoy & Coombs 1999) for Autumn (o) and Spring (Δ) initial disturbance. The median projected time to extinction was estimated from the bootstrapped projection matrix applied to the quantity of J1 individuals present in 1987. The simulated time of extinction was the time step before there was <1 individual present in any of the stage classes. Where populations in year 4 do not reach 1, the remaining proportions are populations projected or observed to be alive after 4 years.

Discussion

Interspecific plant competition, insect herbivory and time of disturbance interact to govern the persistence of ragwort. The prospective and retrospective analyses of our matrix model diagnose which life cycle transitions are potentially and actually most influential on population growth, the range of community configurations over which the diagnosis applies, and whether treatments are effective. For ragwort, we recommend land managers encourage interspecific plant competition early in the ragwort life cycle. Where grass is grazed and soil disturbance is minimal, biological control is necessary. The ragwort flea beetle is more effective than the cinnabar moth because the beetle targets the two most influential life cycle transitions while the moth only targets one. In the larger context of invasive species, the LTRE approach is useful to evaluate the suite of interacting factors that determine successful management of invasive species across the range of conditions in the invaded range.

Identifying and Targeting weed Vulnerabilities

Reduced or absent plant competition, absence of specialist herbivores and disturbance, can all promote a ragwort outbreak or invasion. Managers of ragwort invasion cannot reverse all of these conditions. Instead, they need treatments that will provide the quickest decline in population density while ensuring long-term efficacy. No grazing (Unaltered plant competition) will have the greatest impact on ragwort populations (Wardle 1987; Leiss 2011), but the more realistic condition of reduced or absent interspecific competition achieved by moderate grazing will require the use of the ragwort flea beetle to target ragwort’s vulnerable growth to adult (S4) and fertility (F) transitions.

Insect herbivore effects were mostly negative, but the strength of these negative effects varied with competition and disturbance. The cinnabar moth alone can reduce ragwort density, but its effectiveness is contingent and perceived to be weak overall (Roberts & Pullin 2007); the effects of the ragwort flea beetle were generally stronger than the effects of the cinnabar moth in our study. At the demographic level, this is because the ragwort flea beetle suppressed growth to adult (S4) and fertility (F) while the cinnabar moth suppressed only the fertility transition (F). The superiority of the beetle over the cinnabar moth reflects (i) the beetle’s superior behavioural and numerical responses to an increase in host density (Fig. 9 in McEvoy et al. 1993) and (ii) the likelihood that root-feeding beetle attack inflicts a higher ‘per capita’ (per unit biomass) effect than the shoot-feeding cinnabar moth. Removing the background vegetation led to a sudden increase in the ragwort population that temporarily overwhelmed the flea beetle’s behavioural and numerical responses, inducing time delays in the action of flea beetles as regulators of ragwort abundance (Fig. 6). This may suggest sensitivity to initial conditions and an element of stochasticity that should be investigated further.

There was no evidence of interference between multiple herbivore species. When ragwort was released from plant competition, the effect of both insects was equal to or greater than the effect of either insect acting alone, except in one case (Fig. 5a). This may mitigate persistent fears expressed in the literature that enemy interference can lead to reduced success and support the longstanding practice of introducing multiple natural enemy species rather than relying on a single best natural enemy species identified by prerelease screening of candidates (Fournier et al. 2006; Faria, Umbanhowar & McCann 2008). There is the important caveat that multispecies introductions of biological control organisms should be parsimonious (no more than necessary) and complementary (McEvoy & Coombs 2000), based on ecological as well as economic criteria (Louda 2000). Release of the flea beetle alone will inhibit ragwort growth and avoid the release of the cinnabar moth, which can consume nontarget host plant species (Diehl & McEvoy 1990).

Model Robustness

Our linear model with exponential growth applies best to an outbreak species or to an invader entering new territory with plenty of open space. Population growth rate was highly correlated with more conventional measures of population abundance (total plant cover, plant biomass, and number of ragwort adults) (Appendix S3, Supporting Information). While our results from a linear model appear to be quite robust across a broad suite of environmental conditions, ragwort populations are subject to both intraspecific and interspecific density dependence, which probably increases with successional stage. Density-dependent models of invaders can behave quite differently than linear models (Hastings et al. 2005; Caswell 2008), as illustrated by the contrast of linear (Davis et al. 2006) and nonlinear (Pardini et al. 2009) models of garlic mustard Alliaria petiolata populations. It is challenging to conduct a large factorial experiment and simultaneously test for density-dependent effects. However, a factorial experiment can identify key interactions where density-dependent effects may exist and encourage an experimental design that captures both multiple species interactions and nonlinear dynamics.

Our model in its present form excludes key features of ragwort’s life cycle including iteroparity, dormancy and dispersal that tend to average out local unpredictability in the environment. Plant competition and cinnabar moth can slow growth of individual plants and result in more perennials (McEvoy & Rudd 1993), and the perennial pathway becomes important for population persistence. In the absence of inhibition by these factors, rapid growth of individual plants favours biennials – and the predominance of the biennial pathway becomes important for maximizing population growth, as was seen in our study.

We did not collect data in our current study to parameterize the dormancy cycle in the matrix model. When we added a seed bank with time-invariant parameters estimated for each treatment combination from prior experiments (McEvoy et al. 1993), we found quantitative changes (λ increased by a similar amount across treatment combinations, mean 0·37 and SE = 0·18) but no qualitative changes in the ranking of treatments for their effectiveness in reducing ragwort’s population growth rate. This finding does not preclude the possibility that seed banks may influence the prescription for controlling populations in other environments, as seen with similar species (Jongejans et al. 2008), but the disconnection of the seed bank from above-ground ragwort populations is a real possibility if recurrent disturbance is absent.

Similarly, seed dispersal has the potential to introduce new seeds and maintain a ragwort infestation, and recommendations for management may vary depending on a desire to reduce growth or spatial spread of populations. If ragwort reproduction is vital for spread, as it is for invasive thistles (Jongejans et al. 2008), then the ragwort flea beetle is probably affecting both dispersal ability and population growth while the cinnabar moth primarily limits the dispersal capacity. However, further studies are needed to discover how seed bank dynamics and dispersal interact with temporal and spatial heterogeneity of the environment to influence ragwort population dynamics.

A reliable Prescription for Management

We confirm our hypothesis that ragwort’s biennial transitions were generally more influential on population growth rates than other transitions and are more amenable to manipulation by interventions such as increasing herbivory and interspecific plant competition. Management recommendations based mainly on elasticity analysis may be incomplete if they ignore the underlying biotic interactions and interactions with the environment (Crone et al. 2011). For example, the ragwort flea beetle attacks the roots of juvenile plants, and a prospective analysis might predict reduction in the transition from juvenile to adult stages. This prediction underestimates the observed result that the ragwort flea beetle has strong, negative effects on every transition estimated in ragwort’s life cycle. Feeding by cinnabar moth caterpillars ‘induces’ the perennial pathway in the ragwort life cycle; feeding by the ragwort flea beetle targets both weed biennial vulnerabilities (F and S4) and ‘blocks’ the perennial pathway. Targeted disruption of life cycles refines the concept of a target site, from plant parts (shoots, roots, or seeds) to plant life cycle transitions. Targeted life cycle disruption is no panacea: our results for cinnabar moth show that weed vulnerabilities change and must be reassessed as new components (e.g. herbivores or competitors) are added to the ecosystem. The importance of a LTRE designed to examine a range of community configurations is in the ability to generalize across complex interactions and determine whether the recommendations are consistent in multiple contexts (Thomson 2005; Williams & Crone 2006).

Analysis of vulnerable life cycle transitions is best conducted for demographic rates (rates of growth, development, survivorship, reproduction and movement), and these demographic rates may not correspond exactly to our matrix elements. For example, the complex parameter F for fertility combines several demographic rates in the chain from seed to seedling to the juvenile stage J1. The complementarity of the cinnabar moth and the beetle is not fully revealed by our current model, which both target F. Each insect species in our study reduces F, but in different and complementary ways – the cinnabar moth by reducing fecundity and number of viable seeds stored in the seed bank (P. B. McEvoy & M. Huso, unpublished data), and the ragwort flea beetle by reducing survival of juveniles. In future work, the calculation of elasticities should be based on demographic rates rather than matrix elements as emphasized in other studies (Davis et al. 2006; Jongejans et al. 2008), although Franco & Silvertown (2004) conclude that matrix elements and demographic rates often yield similar results.

How sensitive are these conclusions to environmental conditions? The correspondence between our experimental environments and natural environments has been extensively discussed in prior reports (McEvoy & Rudd 1993; McEvoy et al. 1993; McEvoy & Coombs 1999). Admittedly, this study focused on biotic interactions, and the abiotic conditions found in coastal Oregon are a limited representation of the range of conditions under which ragwort occurs around the world. There is a pressing need to learn more about the relative effects of the cinnabar moth, ragwort flea beetle and interspecific plant competition, on ragwort above-ground dynamics in other environments like inland, continental climates of Idaho and Montana, where ragwort has recently invaded. Our results act as a robust hypothesis about what one may expect under different climates, but observational, experimental and modelling studies may be required to elucidate the ‘context dependence’ in complex interactions apparent in other systems (Shea et al. 2010). Now that we know how ragwort populations respond to variation in biotic community configuration, we need to know how commonly ragwort populations encounter each community configuration in the regional successional mosaic.

Even though the cinnabar moth and ragwort flea beetle were first released 40 years ago in the American west, their impacts on ragwort populations continue. Studies of the cinnabar moth and ragwort flea beetle, alone and in combination, have improved our knowledge about how biological control organisms operate, and they remain viable candidates for release in ecosystems where ragwort has invaded. More generally, we have learnt that local elimination of above-ground plants rather than nonzero weed equilibrium is attainable, observable, and predictable. We have learnt that multiple species are not always antagonistic and can complement each other as they target weed vulnerabilities. Lastly, we have learnt that biological control organisms and interspecific competition can be deployed in a coordinated fashion to achieve weed management outcomes, so long as we understand the biotic interactions that control weed density.

Acknowledgements

We gratefully acknowledge the support of the National Science Foundation through grants BSR-8516997 and BSR-9020483, the United State Department of Agriculture through grants 89-383004515 and 90-383005310, and the Agricultural Research Foundation to P.B.M. The suggestions of J. Barney, J.M. Dauer, and two anonymous reviewers improved an earlier version of this manuscript. The opinions expressed are solely those of the authors and do not necessarily represent the views of the reviewers or sponsoring agencies.

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